the possible canonical forms are restricted to the ones below, see Section 5.6 in [1]}. There exists an invertible matrix \(S\)  such that \(S^{-1}AS=A_1\oplus \cdots \oplus A_k\)  and \(S^*HS=H_1\oplus \cdots \oplus H_k\) ,
where the blocks in the canonical form are one of the following types:
